Solve x^4 - 50x^21

Question

Simplify the expression

x^{4} - 50 x^{2}

Evaluate

x^{4} - 50 x^{2} \times 1

Solution

x^{4} - 50 x^{2}

Show Solution

x^{2} (x^{2} - 50)

Evaluate

x^{4} - 50 x^{2} \times 1

Multiply the terms

x^{4} - 50 x^{2}

Rewrite the expression

x^{2} \times x^{2} - x^{2} \times 50

Solution

x^{2} (x^{2} - 50)

Show Solution

x_{1} = - 52, x_{2} = 0, x_{3} = 52

Alternative Form

x_{1} \approx - 7.071068, x_{2} = 0, x_{3} \approx 7.071068

Evaluate

x^{4} - 50 x^{2} \times 1

To find the roots of the expression,set the expression equal to 0

x^{4} - 50 x^{2} \times 1 = 0

Multiply the terms

x^{4} - 50 x^{2} = 0

Factor the expression

x^{2} (x^{2} - 50) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x^{2} - 50 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x^{2} - 50 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 50 = 0

Move the constant to the right-hand side and change its sign

x^{2} = 0 + 50

Removing 0 doesn't change the value,so remove it from the expression

x^{2} = 50

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 50

Simplify the expression

More Steps

Evaluate

50

Write the expression as a product where the root of one of the factors can be evaluated

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

The root of a product is equal to the product of the roots of each factor

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

x = \pm 52

Separate the equation into 2 possible cases

x = 52 x = - 52

x = 0 x = 52 x = - 52

Solution

x_{1} = - 52, x_{2} = 0, x_{3} = 52

Alternative Form

x_{1} \approx - 7.071068, x_{2} = 0, x_{3} \approx 7.071068

Show Solution